System and method to determine chromatic dispersion in short lengths of waveguides using a 3-wave interference pattern and a single-arm interferometer

ABSTRACT

The present invention relates to a system and method to determine chromatic dispersion in short lengths of waveguides using a three wave interference pattern and a single-arm interferometer. Specifically the invention comprises a radiation source operable to emit radiation connected to a means for separating incident and reflected waves; the means for separating incident and reflected waves having an output arm adjacent to a first end of the waveguide; the means for separating incident and reflected waves connected to a detector; a collimating means positioned at a second end of the waveguide; and a reflecting means positioned at a balanced distance from the collimating means operable to reflect a test emission from the radiation source back through the collimating means, the waveguide, and the means for separating incident and reflected waves thereby generating an interference pattern that is recorded by the detector.

FIELD OF THE INVENTION

This invention relates to a system and method to measure chromaticdispersion in short lengths of waveguides using a three waveinterference pattern and a single arm interferometer.

BACKGROUND OF THE INVENTION

One of the main components in a photonic device is a waveguide or anoptical fiber which serves as a low-loss medium for light transmission.An important characteristic of waveguides such as optical fiber is thedispersion that light experiences as it travels inside the waveguide.Dispersion is the phenomenon that causes different frequencies of lightto travel at different velocities. The phenomenon of dispersion iscommonly observed through the spreading of light by a prism. When whitelight, which contains a broad spectrum of frequencies, enters a prismthe different wavelengths are bent at different angles since eachfrequency sees a different index of refraction, a phenomenon firstquantified by Newton in the 17th century. Inside a fiber, this variationin the index of refraction with frequency is what causes the frequencydependence of the velocity.

A more modern example of the phenomenon of dispersion is the affect ithas on the performance of photonic devices used in communicationsystems. In these systems, dispersion, or more specifically second orderdispersion, leads to a broadening of the pulses used to represent 1 or 0in a digital communication system. Pulse broadening causes adjacent bitsto overlap and leads to intersymbol interference. Intersymbolinterference occurs when a pulse is broadened beyond its allocated bitslot to such an extent that it begins to overlap with adjacent bits andit is no longer possible to determine whether or not a specific bitcontains a 1 or a 0.

As a result of intersymbol interference the allocated bit slots must bewidened and this effectively lowers the number of bits that can betransmitted in a given period of time and reduces the system bandwidth.As a result modern communication systems have evolved methods tomitigate the effects of dispersion.

Current methods of countering the effects of dispersion in an opticalfiber use dispersion compensating devices such as chirped fiber Bragggratings and dispersion compensating fiber (DCF). In order toeffectively use these techniques it is important to know the exactmagnitude of the dispersion that is being compensated for. As a result,knowledge of the dispersion in both the transmission system and thedispersion compensation system is important to the design of the overallcommunication system.

Knowledge of dispersion in a waveguide is also significant for the studyof fiber based nonlinear wave interaction phenomena. An optical solitonis a pulse that maintains a constant shape (width) as it propagatesalong a fiber (first order soliton) or has a shape that is periodic withpropagation (higher order soliton). This is due to the fact that theeffects of dispersion and self phase modulation (SPM) are in balance.SPM is the effect whereby the phase of a given pulse is modified by itsown intensity profile. Knowledge of the dispersion in an optical fiberallows for the determination of the required intensity for the formationof an optical soliton. This effect has also been used in the area ofsoliton effect pulse compression where the combination of the chirpingeffect of SPM and subsequent distributed compression effect of negativedispersion is used to compress an optical pulse. Knowledge of dispersionis also important for the study of nonlinear effects such as secondharmonic generation, three-wave mixing and four-wave mixing since itdetermines the interaction lengths between the various wavelengths.Dispersion is particularly important in techniques that aim to extendthis interaction length such as in Quasi Phase Matching (QPM) devices.

Theory on Chromatic Dispersion of a Waveguide

Dispersion is the phenomenon whereby the index of refraction of amaterial varies with the frequency or wavelength of the radiation beingtransmitted through it. The term ‘Chromatic Dispersion’ is often used toemphasize this wavelength dependence. The total dispersion in awaveguide or an optical fiber is a function of both the materialcomposition (material dispersion) and the geometry of the waveguide(waveguide dispersion). This section outlines the contributions of bothmaterial and waveguide dispersion, identifies their physical source anddevelops the mathematical terminology for their description.

Dispersion in a Waveguide

When light is confined in a waveguide or an optical fiber the index is aproperty of both the material and the geometry of the waveguide. Thewaveguide geometry changes the refractive index via optical confinementby the waveguide structure. The refractive index is therefore a functionof both the material and waveguide contributions. For this reason in afiber or a waveguide the index is known as an effective index.

The dispersion parameter, D, which represents second order dispersionsince it describes how the second derivative of the effective indexvaries with respect to wavelength:

$\begin{matrix}{{D\left( \lambda_{o} \right)} = \left. {{- \frac{\lambda_{o}}{c}}\frac{^{2}n_{eff}}{\lambda^{2}}} \right|_{\lambda_{o}}} & {{Eq}.\mspace{14mu} 1}\end{matrix}$

The dispersion parameter is important since it is related to pulsebroadening which greatly limits the bit rate of a communication system.

The dispersion parameter of a waveguide such as an optical fiber isgiven by the total dispersion due to both the material and waveguidecontributions. The total dispersion is the combination of the materialdispersion and the waveguide dispersion and thus the dispersionparameter of a waveguide is given by:

$\begin{matrix}{D = {{{- \frac{2\pi \; c}{\lambda^{2}}}\frac{}{\omega}\left( \frac{1}{V_{G}} \right)} = {D_{M} + D_{W}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

The next two sections discuss the contributions that both material andwaveguide dispersion make individually to the total dispersion.

Material Dispersion

Material dispersion originates from the frequency or wavelengthdependent response of the atoms/molecules of a material toelectromagnetic waves. All media are dispersive and the onlynon-dispersive medium is a vacuum. The source of material dispersion canbe examined from an understanding of the atomic nature of matter and thefrequency dependent aspect of that nature. Material dispersion occursbecause atoms absorb and re-radiate electromagnetic radiation moreefficiently as the frequency approaches a certain characteristicfrequency for that particular atom called the resonance frequency.

When an applied electric field impinges on an atom it distorts thecharge cloud surrounding that atom and induces a polarization that isinversely proportional to the relative difference between the frequencyof the field and the resonance frequency of the atom. Thus the closerthe frequency of the electromagnetic radiation is to the atoms resonancefrequency the larger the induced polarization and the larger thedisplacement between the negative charge cloud and the positive nucleus.

The material dispersion is then determined by taking the derivative ofthe group index of the material with respect to wavelength orequivalently the second derivative of the absolute index with respect towavelength:

$\begin{matrix}{D_{M} = {{\frac{1}{c}\frac{N_{G}}{\lambda}} = {{- \frac{\lambda}{c}}\left( \frac{^{2}n}{\lambda^{2}} \right)}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

Waveguide Dispersion

Waveguide dispersion occurs because waveguide geometry variably affectsthe velocity of different frequencies of light. More technically,waveguide dispersion is caused by the variation in the index ofrefraction due to the confinement of light in an optical mode. Waveguidedispersion is a function of the material parameters of the waveguidesuch as the normalized core-cladding index difference,Δ=(n_(core)−n_(cladding))/n_(core) and geometrical parameters such asthe core size, a. The index in a waveguide is known as an effectiveindex, n_(eff), because of the portion of the index change caused bypropagation in a confined medium.

Confinement is best described by a quantity known as the V parameter,which is a function of both the material and geometry of the waveguide.The V parameter is given by Eq. 4:

$\begin{matrix}{{V(\lambda)} = {{\frac{2\pi}{\lambda}{a\left( {n_{core}^{2} - n_{cladding}^{2}} \right)}^{1/2}} \approx {\frac{2\pi}{\lambda}{an}_{core}\sqrt{2\Delta}}}} & {{Eq}.\mspace{11mu} 4}\end{matrix}$

Propagation in a waveguide is described by a quantity known as thenormalized propagation constant, b, which is also a function of thematerial and geometry of the waveguide. This quantity is given in Eq. 5:

$\begin{matrix}{b = \frac{n_{eff} - n_{cladding}}{n_{core} - n_{cladding}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

The contribution of the waveguide to the dispersion parameter depends onthe confinement and propagation of the light in a waveguide and hence itis a function of both the V parameter and the normalized propagationconstant, b. The waveguide dispersion can be calculated via knowledge ofV and b via Eq. 6:

$\begin{matrix}{D_{W} = {- {\frac{2\pi}{\lambda^{2}}\left\lbrack {{\frac{N_{G{({cladding})}}^{2}}{n_{cladding}\omega}\frac{V{^{2}({Vb})}}{V^{2}}} + {\frac{N_{G{({cladding})}}^{2}}{\omega}\frac{({Vb})}{V}}} \right\rbrack}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

In most cases the main effect of the waveguide dispersion in standardsingle mode fibers is a reduction in dispersion compared to dispersionin bulk. In comparison to material dispersion the contribution ofwaveguide dispersion is quite small and in most standard single modefibers it only shifts the zero dispersion wavelength from 1276 nm to1310 nm.

In summary, the dispersion in a waveguide or an optical fiber is causednot only by the material but also by the effect of confinement andpropagation in the waveguide. Thus accurate knowledge of the dispersionin a waveguide cannot be made by simple knowledge of the materialdispersion but must include the effect of the waveguide. As a resulteither the dimensions of the waveguide must be known to a high degree ofaccuracy so that the waveguide dispersion can be calculated (which isnot easy since fabrication processes are hardly perfect) or thedispersion must be measured empirically. Accurate measurement of the(total) dispersion parameter, D, is important to the design of photonicsystems.

Polarization Mode Dispersion

In addition to the above, optical waveguides may suffer frompolarization mode dispersion (PMD). PMD may exist in fibers withasymmetrical cores. In optical fibers, the light that travels along oneof the two polarization axis travels at a right angle to light travelingalong the other axis. In asymmetrical optical fibers, the light travelsalong the two axes at different speeds. This causes pulses to spread,which can cause them to become undetectable at the detector.

Conventional Measurement Techniques

There are 3 categories of dispersion measurement techniques: Time offlight (TOF), Modulation phase shift (MPS) and Interferometric. TOF andMPS are the most widely used commercial dispersion measurementtechniques. Interferometric techniques are not widely used commerciallybut have been used in laboratories for dispersion measurements.Interferometric techniques come in two forms; temporal and spectral. Theexisting techniques differ in measurement precision and fiber lengthrequirements.

Time of Flight Technique

In the TOF technique the second order dispersion parameter, D, hereafterreferred to simply as the dispersion parameter, can be determined eitherby measuring the relative temporal delay between pulses at differentwavelengths or by measuring the pulse broadening itself. The relativetemporal delay between pulses at different wavelengths is measured todetermine the group velocity which can then be used to determine thedispersion parameter using Eq. 7:

$\begin{matrix}{{D\left( \lambda_{o} \right)} = \frac{\Delta \; t}{L\; \Delta \; {\lambda \left( \lambda_{o} \right)}}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

The above equation can also be used to determine the dispersionparameter from the pulse broadening itself if Δt is the measured pulsebroadening and Δλ is the bandwidth of the wavelengths in the pulse. Themeasurement precision achievable by the TOF technique is on the order of1 ps/nm.

One of the main problems with the TOF technique is that it generallyrequires several kilometers of fiber to accumulate an appreciabledifference in time for different wavelengths. Another issue with the TOFtechnique when the pulse broadening is measured directly is that thepulse width is affected by changes in the pulse shape which leads toerrors in the measurement of the dispersion parameter. As a result, inorder to measure the dispersion parameter with a precision near 1ps/nm-km several kilometers of fiber are required.

Modulation Phase Shift Technique

The MPS technique is another dispersion characterization technique thatrequires long lengths of fiber. In the MPS technique, a continuous-waveoptical signal is amplitude modulated by an RF signal, and thedispersion parameter is determined by measuring the RF phase delayexperienced by the optical carriers at the different wavelengths.

The RF phase delay information is extracted by this technique, and bytaking the second derivative of the phase information, the dispersionparameter can be determined. Measurement precision achievable by the MPStechnique is on the order of 0.07 ps/nm. Due to its higher precision,MPS has become the industry standard for measuring dispersion in opticalfibers. However, MPS has several disadvantages. The first is that it isexpensive to implement since the components required such as an RFanalyzer and a tunable laser, are costly. The second is that itsprecision is limited by both the stability and jitter of the RF signal.

MPS has several limitations on the minimum device length that it iscapable of characterizing. In the MPS method the width of the modulatedsignal limits the minimum characterizable device length. This methodalso typically requires fiber lengths in excess of tens of meters toobtain a precision to better than 1 ps/nm-km. Therefore it is notdesirable for the characterization of specialty fibers or gain fibers,of which long fiber lengths are expensive to acquire or not available.Also, when fiber uniformity changes significantly along its length, thedispersion of a long span of fiber cannot be used to accuratelyrepresent that of a short section of fiber. In such cases, dispersionmeasurement performed directly on short fiber samples is desirable. As aresult a technique for measuring the dispersion of short lengths offiber is desired.

Dispersion Measurements on Short Length

Interferometric techniques are capable of characterizing the dispersionon fiber lengths below 1 m. There are two categories of interferometrictechniques for making dispersion measurements on fiber of short length:temporal and spectral.

Temporal Interferometry (Fourier Transform Spectroscopy)

Dual Arm temporal interferometry employs a broadband source and avariable optical path to produce a temporal interferogram between afixed path through the test fiber and variable air path. It involvesmoving one arm of the interferometer at a constant speed and plottingthe interference pattern as a function of delay length (time). Thespectral amplitude and phase are then determined from the Fouriertransform of the temporal interferogram.

A temporal interferogram gives the phase variation as a function oftime. The spectral phase variation can be extracted from the temporalinterferogram if a Fourier Transform is applied to it. The spectralphase contains the dispersion information which can be indirectlyobtained by taking the second derivative of the spectral phase. Aprecision of 0.0015 ps/nm measured on a 0.814-m-long photonic crystalfiber was recently reported using temporal interferometry. The maindisadvantage of temporal interferometry is that it is susceptible tonoise resulting from both translation inaccuracy and vibration of theoptics in the variable path. A tracking laser is typically required tocalibrate the delay path length. Another problem with this technique isthat a second derivative of the phase information must be taken toobtain the dispersion parameter which means that it is less accuratethan a method that can obtain the dispersion parameter directly.

Spectral Interferometry

Spectral interferometry, like temporal interferometry, is capable ofcharacterizing the dispersion in short length fiber (<1 m). In spectralinterferometry, instead of stepping the length of one of the arms, ascan of the wavelength domain performed to produce a spectralinterferogram. Spectral interferometry is generally more stable thantemporal interferometry since the arms of the interferometer are keptstationary. Thus it is simpler than temporal interferometry since notracking laser is necessary.

There are two types of spectral interferometry, one is general and doesnot require balancing, and another, the special case, is ‘balanced’. Inthe balanced case it is possible to directly measure the dispersionparameter from the interferogram. This makes it more accurate thantemporal interferometry and it is for this reason that spectralinterferometry is discussed as a dispersion measurement technique.

In general spectral interferometry the dispersion parameter is obtainedfrom the interference spectrum produced by two time delayed lightpulses/beams in an unbalanced dual arm interferometer. Two pulses/beamsfrom the two arms of the interferometer are set up to interfere in aspectrometer and a spectral interferogram is produced. The interferencepattern produced for a given time or phase delay is given by:

$\begin{matrix}\begin{matrix}{{I(\omega)} = {{{E_{o}(\omega)} + {{E(~\omega)}{\exp \left( {{\omega}\; \tau} \right)}}}}^{2}} \\{= {{{E_{o}(\omega)}}^{2} + {{E(\omega)}}^{2} + {{E_{o}^{*}(\omega)}E\; {\omega (\omega)}{\exp ({\omega\tau})}} +}} \\{{{E_{o}(\omega)}{E^{*}(\omega)}{\exp \left( {- {\omega\tau}} \right)}}} \\{= {{{E_{o}(\omega)}}^{2} + {{E(\omega)}}^{2} + {{f(\omega)}{\exp ({\omega\tau})}} +}} \\{{{f^{*}(\omega)}{\exp \left( {- {\omega\tau}} \right)}}}\end{matrix} & {{Eq}.\mspace{14mu} 8}\end{matrix}$

The last two terms in Eq. 8 result in spectral interference pattern viaa cos(Δφ(ω)+ωτ) term.

There are several ways to extract the phase information from the cosineterm but the most prevalent way to do so is to take the Inverse Fouriertransform of the spectral interference pattern. Note thatf(ω)=F.T.f(t)=|E*_(o)(ω)E(ω)|exp(iΔφ(ω)) contains all the phaseinformation on the spectral phase difference Δφ(ω). Therefore, if f(ω)can be extracted from the interference pattern then the phase differenceinformation can be known. If an Inverse Fourier Transform of thespectral interference is performed on the interference pattern thefollowing is obtained:

F.T. ⁻¹(I(ω))=E* _(o)(−t){circumflex over (x)}E_(o)(t)+E*(−t){circumflex over (x)}E(t)+f(t−τ)+f(−t−τ)  Eq. 9

If all terms except the f (t−τ) term get filtered out via a band passfilter then the phase information can be extracted from a FourierTransform on f (t−τ).

The phase information can then be extracted by applying a FourierTransform to the filtered component f(t−τ) thereby transferring it backto the spectral domain. The complex amplitude therefore becomesf(ω)=|E_(o)(ω)∥E(ω)|exp(iΔφ(ω)+ωr). The phase of this complex amplitudeminus the linear part (ωτ) that is due to the delay, yields the spectralphase difference between the two pulses as a function of w and isindependent of the delay between the two pulses. In this way the phasedifference between the two pulses can be obtained.

If one of the pulses travels through a non-dispersive medium such as airand the other pulse travels through a dispersive medium such as anoptical fiber then the phase difference spectrum will be directlyrelated to the dispersion in the fiber. Thus the dispersion parameterplot can be determined by taking the second derivative of the phasedifference spectrum with respect to wavelength.

The main issue with this form of spectral interferometry, however, isthat the dispersion parameter is not determined directly but rather viaa second order derivative of the phase information with respect towavelength. Therefore, like temporal interferometry, this generalunbalanced method of spectral interferometry is not as accurate as thebalanced method capable of measuring the dispersion parameter directlyof the present invention.

In balanced spectral interferometry the arm lengths of an interferometerare kept constant and they are balanced for a given wavelength calledthe central wavelength such that the group delay in both arms is thesame. This allows for the removal of the effect of the large lineardispersion term in the interferogram. Balanced interferometry measuresthe dispersion parameter D at the wavelength at which the group delay isthe same in both arms. This wavelength is henceforth referred to as thecentral wavelength. The dispersion parameter in this case can bedirectly determined from the phase information in the spectralinterferogram without differentiation of the phase. For this reason itis more accurate than both unbalanced general spectral interferometryand temporal interferometry. As a result balanced spectralinterferometry is often used to obtain accurate dispersion measurementsin short length waveguides and fibers.

Both forms of spectral interferometry are considered to be lesssusceptible to noise since the arms of the interferometer are kept stilland there are no moving parts. It is for this reason that spectralinterferometry in general is considered to be more accurate thantemporal interferometry. Spectral interferometry is therefore consideredto be the technique of choice for measuring the dispersion of photoniccomponents and spectral depth resolved optical imaging. One well knownand important class of spectral interferometry is optical coherencetomography (OCT).

Balanced dual arm spectral interferometers are typically found in aMichelson or a Mach-Zehnder configuration in which the path lengths areequalized at the given wavelength in which the dispersion is to bemeasured. The most often used configuration, however, is the Michelsonand the discussion that follows considers the Michelson interferometer.In a balanced Michelson interferometer the dispersion is measured fromthe interference between two waves: one that passes through the testfiber and another that passes through an air path. Balancing the airpath length with the fiber eliminates the effect of the group index ofthe fiber in the interference pattern. This allows for the measurementof the second derivative of the effective index with respect towavelength directly from the interference pattern.

The main disadvantage of this Michelson configuration is that two typesof path balancing must occur simultaneously. The first type of pathbalancing is coupler arm balancing wherein the coupler arms need to bebalanced exactly or an extra set of interference fringes will be createdfrom the reflections at the two end facets of the coupler arms as shownin FIG. 1.

The second type of balancing is test fiber-air path balancing to ensurethat the optical path length in the air path exactly equals that of thefiber for a given central wavelength. This ensures that the centralwavelength in the interference pattern is within the viewable bandwidthof the OSA.

The main problem in implementing a Michelson interferometer is that thearms of the coupler cannot be balanced exactly and as a result theeffect of the extra set of reflections produced at the coupler facetscannot be removed.

Comparison of Dispersion Measurement Techniques

There have been several techniques developed for the measurement ofchromatic dispersion in fiber. Especially important are those developedfor the measurement of short lengths of fiber. One reason that shortlength characterization techniques are important stems from recentdevelopments in the design and fabrication of specialty fiber.

Specialty fiber such as Twin Hole Fiber (THF) (FIG. 14) and PhotonicCrystal Fiber (PCF) have made short length fiber characterizationdesirable due to their high cost. Because of this it is not economicalto use TOF and MPS techniques to characterize these types of fiber.Another impetus for short length characterization comes from the factthat in many specialty fibers the geometry is often non-uniform alongits length. As a result of this non-uniformity the dispersion in thesefibers varies with position. Thus measurement of the dispersion in along length of this fiber will be different than that measured in asection of the same fiber.

Based on the above discussion, the technique of choice for dispersionmeasurement is balanced spectral interferometry since it will providethe most accurate measurements. As a result the new technique willemploy balanced spectral interferometry.

The two important parameters in comparing dispersion measurementtechniques are the minimum device length that each is capable ofcharacterizing and the precision to which the characterization isachieved. It is generally desirable to characterize as short a fiber aspossible with as high a precision as possible. It is also desirable toperform the measurement in the simplest way possible.

Therefore, what is needed is a new method for the measurement ofdispersion that does not require the cancellation of any extra fringes.What is also needed is a method to measure the dispersion parameter inshort lengths of optical fiber. The initial need for a short lengthcharacterization scheme came from the need to measure the dispersion ofa specialty fiber such as THF, PCF, or gain fibre. This requirement isbased on the expense of fibre, nonlinear wave interaction phenomena infibre, and non-uniform dispersion along the length of a fibre.

SUMMARY OF THE INVENTION

According to the present invention, a system and method to determinechromatic dispersion in short lengths of waveguides using a three waveinterference pattern and a single-arm interferometer has been developed.

In a first aspect, the present invention relates to an interferometersystem for obtaining a measure of the chromatic dispersion of awaveguide comprising a radiation source operable to emit radiationconnected to a means for separating incident and reflected waves; themeans for separating incident and reflected waves having an output armadjacent to a first end of the waveguide; the means for separatingincident and reflected waves further connected to a detector; acollimating means positioned at a second end of the waveguide; and areflecting means positioned at a balanced distance from the collimatingmeans operable to reflect a test emission from the radiation source backthrough the collimating means, the waveguide, and the means forseparating incident and reflected waves thereby generating aninterference pattern that is recorded by the detector;

In a second aspect of the present invention said interference patternconsists of three waves wherein a first wave is a reflection of the testemission from one facet of the waveguide, a second wave is a reflectionof the test emission from a second facet of the waveguide and a thirdwave is a reflection of the test emission from the reflecting means.

In another aspect, the present invention relates to an interferometricmethod for obtaining a measure of the chromatic dispersion of awaveguide comprising the steps of:

-   -   a. connecting a radiation source to a means for separating        incident and reflected waves, said means for separating incident        and reflected waves having an output arm terminating at a        connector;    -   b. placing a first facet of the waveguide adjacent to the        connector;    -   c. connecting the means for separating incident and reflected        waves to a detector;    -   d. placing a collimating lens at a second facet of the        waveguide;    -   e. positioning a reflecting means at a balanced distance from        the collimating lens;    -   f. generating a radiation emission from the radiation source;    -   g. recording an interferogram consisting of three waves with the        detector wherein the first wave is a reflection of the radiation        emission from the first facet of the waveguide, the second wave        is a reflection of the radiation emission from the second facet        of the waveguide, and the third wave is a reflection of the        radiation emission from the reflecting means; and    -   h. measuring dispersion parameters from the recorded        interferogram.

In a still further aspect of the present invention relates to a methodfor increasing a maximum length of a waveguide for which chromaticdispersion may be measured using an interferometer comprising the stepsof:

-   -   a. generating an interferogram including sampling a radiation        intensity at each of a set of wavelengths, each said wavelength        separated by a step size of a tunable laser;    -   b. selecting a set of wavelength windows, each said wavelength        window including a portion of the interferogram corresponding to        one or more of said wavelengths, the set of wavelength windows        encompassing the whole of the interferogram, the set of        wavelength windows not overlapping at any given portion of the        interferogram;    -   c. selecting a maximum radiation intensity measured in each of        said wavelength windows; and    -   d. connecting the maximum radiation intensities of each said        wavelength window together to form a wavelength envelope.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood with reference to the drawings.

The accompanying drawings, which are incorporated in and constitute apart of the specification, illustrate various example systems andmethods and are not intended to limit the scope of the specification.

FIG. 1 illustrates the interference caused by coupler arm reflectionsfor a Michelson interferometer.

FIG. 2 illustrates a single-arm interferometer that generates athree-wave interferogram.

FIG. 3 illustrates the source of three waves comprising aninterferogram.

FIG. 4 illustrates an example of an interferogram produced from threeinterfering waves using an example fibre.

FIG. 5 illustrates the minimum required source bandwidth and thelocations of the troughs required to extract dispersion information froman interferogram.

FIG. 6 illustrates the minimum fibre length required to extractdispersion information for a given source bandwidth.

FIG. 7 illustrates the method of wavelength windowing.

FIG. 8 illustrates the measured probability density function and aGaussian fit for the step size of an example tunable laser.

FIG. 9 illustrates the probability density functions for the step sizeand the carrier for determining the probability of hitting a peak in agiven wavelength window.

FIG. 10 illustrates the relationship between the probability that atleast one peak is sampled in a given window and fibre length.

FIG. 11 illustrates a system comprising a single arm interferometer,tunable laser source and detector.

FIG. 12 illustrates the experimental results of dispersioncharacterization using a single arm interferometer.

FIG. 13 illustrates the experimental results of dispersioncharacterization using a single arm interferometer.

FIG. 14 illustrates the cross section of a typical twin-hole fibre.

FIG. 15 illustrates the experimental results of dispersioncharacterization using a single arm interferometer.

FIG. 16 illustrates an embodiment of a dispersion measurement module fora tunable laser system.

DETAILED DESCRIPTION OF THE INVENTION System Operation 1: Development ofSingle Arm Interferometry

A Single Arm Interferometer (SAI) can be produced by folding the twoarms of a Michelson interferometer (FIG. 1) together into a single pathand placing a mirror behind the test fiber. This configuration wasdesigned to eliminate the calibration step required by dual arminterferometers in which the coupler arms are made to bedisproportionate in length to eliminate the effect of the extrareflections from the coupler-test fiber/coupler-air path facets. Sincecalibration is not required this technique is also more accurate than adual arm interferometer.

1 1 A New Concept

A balanced Single-Arm Interferometer (SAI) can directly measuredispersion in short fibers. A balanced SAI is depicted in FIG. 2. Theradiation source (11) (“source”) generates an optical signal that entersa device operable to separate the incoming and reflected waves. Thisdevice may be a circulator (13), coupler, or other wave-separatingmeans. The optical signal then travels through the launch fiber (15) tothe adjacently placed test fiber (17) by way of an angle polishedconnector (25) that is operable to minimize reflection at the end facetof the launch fiber (15). The optical signal then travels through thetest fiber (17) and passes through a collimating means (19) as shown inFIG. 11. Finally, the collimated signal reflects off a mirror (21) andback through the collimating means (19), test fiber (17), launch fiber(15), and wave-separating means. The wave-separating means is operableto direct the reflected optical signal to the detector (23), whichrecords the interference pattern produced by the reflections from thefirst U_(o) and second U₁ facets of the test fiber (17) and thereflection U₂ from the mirror (21).

The SAI system may operate in several different embodiments, the source(11)/detector (23) pairing may be a broadband source operable with anOptical Spectrum Analyzer (OSA) or the source (11)/detector (23) pairingmay be a tunable laser (31) operable with a detector (23) system.

The test fiber (17) is a waveguide. As previously mentioned waveguidesencompass a large class of materials and include but are not limited tothe following: optical fiber, photonic crystal fiber, nanowire,nanofiber, twin-hole fiber and etched waveguides.

This configuration is not only much simpler than a dual arminterferometer but as further evidenced by the experimental setupdetailed in FIG. 11, it also minimizes the need for system calibration(assuming the dispersion introduced by the collimating lens (19) isnegligible and the air path L_(air) is stable). Its simpler constructionalso makes it less susceptible to polarization and phase instabilities.

The SAI is a balanced interferometer since the group delay in the testfiber (17) is the same as the group delay in the air path (27). It willbe shown mathematically that this balancing of the group delay in eachpath (17, 27) allows the dispersion parameter to be measured directlyfrom the interference pattern. The conceptual difference between SAI andDual Arm interferometers is that, in SAI, the interference pattern isproduced by three waves: two from the reflections (U_(o), U₁) at thefacets of the test fiber (17) and one (U₂) from a mirror (21) placedbehind it (as shown by U_(o), U₁, and U₂ in FIGS. 2 and 3). The beatingbetween the interference fringes produced by the test fiber (17) andthose by the air path (27) generates an envelope which is equivalent tothe interference pattern produced by two waves (U₁ and U₂ in FIGS. 2, 3)in a dual-arm interferometer.

From the phase information in this envelope the dispersion parameter canbe extracted. Both dual and single arm balanced interferometers have incommon this ability to directly measure the dispersion parameter fromthe interference pattern.

Optionally, the launch fiber (15) may be configured as a polarizationcontroller. This may be accomplished by a number of means known to thoseskilled in the art, such as looping the launch fiber (15) into threecoils. Alternately, the polarization controller may be implemented byplacing a linear polarizer in the air path (27). By providing apolarization controller, the SAI may be operable to measure PMD.

The SAI configuration appears similar to common path interferometers,often used for depth imaging as in Common-Path Optical CoherenceTomography (CP-OCT). The SAI, however, is fundamentally different fromCP-OCT since it utilizes 3 reflections (U_(o), U₁, and U₂), and extractsthe dispersion parameter directly from the envelope of the interferencepattern. The differences between the Michelson Interferometer, CP-OCTand balanced Single Arm Interferometry are outlined in Table 1.

TABLE 1 Differences & Similarities between the Michelson Interferometer,CP-OCT and the Single Arm Interferometer Balanced MichelsonInterferometer CP-OCT Balanced SAI # of interfering waves 2 2 3 # oflongitudinally 2 1 1 separate paths Path balancing yes no yes Dispersionentire n/a envelope of information interferogram interferogramDispersion parameter directly n/a directly measured Measures dispersionoptical path dispersion parameter length parameter difference

1.2 Mathematical Description 1.2.1.1 Equal Amplitude Case

Dispersion measurements can be made using a single-arm interferometer byextracting the second derivative of the effective index with respect towavelength from the envelope of the interference pattern generated bythree waves U_(o), U₁ and U₂ depicted in FIGS. 2 and 3.

The extra reflection from the launch fiber (15) is minimized using anglepolished connector (25) as shown in FIGS. 2, 3 and further addressed inthe experimental set-up found in FIG. 11. The angle polished connector(25) is used at the junction with the test fiber (17). It should benoted that this method is insensitive to the loss introduced by theangle polished connector (25) since the dispersion information iscontained within the phase of the three reflected waves (U_(o), U₁, andU₂). The optical path length of the air path L_(air) is made to cancelout the strong linear effective group index term of the test fiber (17)at a central wavelength, λ_(o). The amplitudes of U_(o) and U₁ areassumed to be equal to the magnitude of the reflection at the test fiber(17) end facets. The amplitude of U₂ depends on the amount of lightcoupled back to the test fiber (17). This coupling efficiency can beadjusted by varying the alignment of the mirror (21) such that U₂ hasthe same amplitude as U_(o) and U₁. In this simplified presentation:

U₁=U₀e^(−j2βL) ^(f)

U₂=U₀e^(−j2βL) ^(f) ^(−j2k) ⁰ ^(L) ^(air)   Eq. 10

In Eq. 10, L_(f) and L_(air) are the lengths of the test fiber (17) andthe air path (27), respectively. β and k_(o) are the propagationconstant of the fundamental mode in the fiber and the propagationconstant in free space. The interference pattern is produced by theinterference of the three reflections (U_(o), U₁, and U₂) is given byEq. 11:

$\begin{matrix}\begin{matrix}{I_{o} = {{U_{0} + U_{1} + U_{2}}}^{2}} \\{= {U_{o}^{2}\begin{pmatrix}{3 + {2{\cos \left( {{2\beta \; L_{f}} + {2k_{o}L_{air}}} \right)}} +} \\{4\cos \; \left( {{\beta \; L_{f}} + {k_{o}L_{air}}} \right){\cos \left( {{\beta \; L_{f}} - {k_{o}L_{air}}} \right)}}\end{pmatrix}}}\end{matrix} & {{Eq}.\mspace{14mu} 11}\end{matrix}$

Eq. 11 contains two fast terms, with a phase φ₁=+(βL_(f)+k_(o)L_(air))and φ₂=2(βL_(f)+k_(o)L_(air)). Since φ₁ is slower than φ₂ it willamplitude modulate the faster term. As a result the period of the‘carrier’ will be that of the slowest of the fast terms, φ_(carrier)=φ₁.This carrier is then itself amplitude modulated by the slower termφ_(envelope)=(βL_(f)−k_(o)L_(air)) to produce the ‘envelope’ of theinterference pattern. This envelope is equivalent to the interferencepattern produced by Michelson interferometer and it can be written as:

U_(o) ²(5+4|cos(φ_(envelope))|)  Eq. 12

The calculated interference pattern generated by the setup for a 39.5 cmSMF28™ test fiber is illustrated in FIG. 4. It depicts the envelopefunction which is a close approximation of the envelope of the actualenvelope of the carrier.

Applying a Taylor expansion to the phase of the slow envelope andreplacing β with 2πn_(eff)/λ, where n_(eff) is the effective index ofthe fiber, gives the phase relation in Eq. 13:

$\begin{matrix}{{\varphi_{envelope}(\lambda)} = {2\pi \begin{Bmatrix}{{{\frac{1}{\lambda}\begin{bmatrix}\left( \left. {{n_{eff}\left( \lambda_{o} \right)} - {\lambda_{o}\frac{n_{eff}}{\lambda}}} \right|_{\lambda_{o}} \right) \\{L_{f} - L_{air}}\end{bmatrix}} +}\mspace{11mu}} \\\left. {L_{f}\frac{n_{eff}}{\lambda}} \middle| {}_{\lambda_{o}} + \right. \\\left. {L_{f}\frac{\left( {\lambda - \lambda_{o}} \right)^{2}}{{2!}\lambda}\frac{^{2}n_{eff}}{\lambda^{2}}} \middle| {}_{\lambda_{o}} + \right. \\{\left. {L_{f}\frac{\left( {\lambda - \lambda_{o}} \right)^{3}}{{3!}\lambda}\frac{^{3}n_{eff}}{\lambda^{3}}} \middle| {}_{\lambda_{o}}{+ \ldots} \right.\;}\end{Bmatrix}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

The first term in Eq. 13 (in the square brackets) disappears whenL_(air) is adjusted to balance out the group delay of the test fiber(17) at λ_(o), the balanced wavelength. Taking the difference betweenthe phases at two separate wavelengths; λ₁ and λ₂ results in:

$\begin{matrix}\begin{matrix}{{\Delta\varphi}_{envelope} = {{{\varphi_{envelope}\left( \lambda_{2} \right)} - {\varphi_{envelope}\left( \lambda_{1} \right)}}}} \\{= {2{\pi \begin{pmatrix}\left. {\left\lbrack {\frac{\left( {\lambda_{2} - \lambda_{0}} \right)^{2}}{{2!}\lambda_{2}} - \frac{\left( {\lambda_{1} - \lambda_{0}} \right)^{2}}{{2!}\lambda_{1}}} \right\rbrack \frac{^{2}n_{eff}}{\lambda^{2}}} \middle| {}_{\lambda_{0}} + \right. \\\left. {\left\lbrack {\frac{\left( {\lambda_{2} - \lambda_{0}} \right)^{3}}{{3!}\lambda_{2}} - \frac{\left( {\lambda_{1} - \lambda_{0}} \right)^{3}}{{3!}\lambda_{1}}} \right\rbrack \frac{^{2}n_{eff}}{\lambda^{3}}} \right|_{\lambda_{0}}\end{pmatrix}}L_{f}}} \\{= {m\; \pi}}\end{matrix} & {{Eq}.\mspace{14mu} 14}\end{matrix}$

Note that m is the number of fringes between the two wavelengths. Ifthis phase difference is taken using a different pair of peaks/troughs(i.e. λ₃ & λ₄) the result is a system of equations in whichd²n_(eff)/dλ²|_(λ) _(o) and d³n_(eff)/dλ³∥_(λ) _(o) can be solveddirectly. Since the troughs in the interference pattern are more sharplydefined it is more accurate to choose the wavelength locations of thetroughs of the envelope as the wavelengths used in Eq. 14.

Note that, if the third-order dispersion is ignored, then only twowavelengths (e.g. λ₁ and λ₂) are required to calculate the second-orderdispersion. This, however, would be less accurate. The dispersionparameter D can then be found as follows:

$\begin{matrix}{{D\left( \lambda_{o} \right)} = \left. {{- \frac{\lambda_{o}}{c}}\frac{^{2}n_{eff}}{\lambda^{2}}} \right|_{\lambda_{o}}} & {{Eq}.\mspace{14mu} 15}\end{matrix}$

1.2.1.2 Unequal Amplitude Cases

In reality the reflections (U_(o), U₁, and U₂) from the three facets ofthe interferometer as illustrated in FIGS. 2 and 3 do not have equalmagnitudes. As a result the interference pattern produced by thesereflections (U_(o), U₁, and U₂) is not as simple as presented in theprevious section. It is shown that despite this fact the previousresults still hold since the locations of the troughs of the envelope,which are used to obtain the dispersion information, remain the sameeven though the fringe contrast varies.

In general the reflections from each facet (U_(o), U₁) of the test fiber(17) and the reflection from the mirror (U₂) shown in FIG. 3, do nothave the same magnitude. The magnitudes of the reflections in terms ofthe first reflection (U_(o)) can be expressed as follows:

U₁=aU₀e^(−j2βL) ^(f)

U₂=bU₀e^(−j2βL) ^(f) ^(−j2k) ⁰ ^(L) ^(air)   Eq. 16

In Eq. 16 L_(f) and L_(air) are the lengths of the test fiber (17) andthe air path (27), respectively. β and k_(o) are the propagationconstant of the fundamental mode in the fiber and the propagationconstant in free space. ‘a’ is the fraction of the amplitude reflectedfrom the second facet in terms of the first and ‘b’ is the fraction ofthe amplitude reflected from the mirror (21) in terms of the fractionreflected from the first facet. The interference pattern of the spectralinterferogram can be expressed as:

$\begin{matrix}\begin{matrix}{I_{o} = {{U_{0} + U_{1} + U_{2}}}^{2}} \\{= {U_{o}^{2}\begin{Bmatrix}{1 + a^{2} + b^{2} + {4a\; {\cos \left( {{\beta \; L_{f}} + {k_{o}L_{air}}} \right)}}} \\{{\cos \left( {{\beta \; L_{f}} - {k_{o}L_{air}}} \right)} +} \\{{2{a\left( {b - 1} \right)}{\cos \left( {2k_{o}L_{air}} \right)}} +} \\{2b\; {\cos \left( {2\left( {{\beta \; L_{f}} + {k_{o}L_{air}}} \right)} \right)}}\end{Bmatrix}}}\end{matrix} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

The expression in Eq. 17 can be treated as a fast-varying “carrier”(with respect to frequency or wavelength) modified by an upper and alower slow-varying envelope, as shown in FIG. 4, which depicts thesimulated spectral interferogram generated by the 3-wave SAI with a39.5-cm SMF28 fiber as the test fiber. Upon closer examination (FIG. 4,lower right), the “carrier” is not a pure sinusoidal function, becausethere are three fast-varying phases in Eq. 17, 2(βL_(f)+k_(o)L_(air)),(βL_(f)+k_(o)L_(air)), and 2k_(o)L_(air), all of which vary much fasterthan the phase of the envelope (φ_(envelope)), which equalsβL_(f)−k_(o)L_(air). When b is large (>0.5), it can be shown that theupper envelope is approximated by

U _(o) ²(1+a ² +b ²+2a(b−1)+2b+4a|cos(φ_(envelope))|)  Eq. 18

It will now be shown that although the magnitude of the interferencepattern is not the same as the envelope for cases in which b≠1, the peakand trough locations of the two match exactly. As a result the phaseinformation of the interferogram is preserved and the dispersioninformation can be extracted from the interferogram. Note that a=b=1 isa special case of this more general analysis and was presented in theprevious section.

Since the phase of the upper envelope, φ_(envelope) (and therefore thedispersion information) is unaffected by the magnitude of thereflections from the facets (U_(o), U₁) and the mirror (U₂), the methodfor determining the dispersion parameter as presented in Eqs. 13 to 15is valid even in the general case. The dispersion parameter, therefore,can always be obtained from an SAI.

As mentioned earlier, the main difference between the fringes producedin the SAI and those produced by dual arm interferometers is thepresence of a fast carrier (Eq. 17) slowly modulated by the desiredenvelope. The presence of this carrier sets extra operationalconstraints that will be discussed in the next section.

1.3 System Parameters

There may be four factors of interest with regard to the dispersionmeasurement of the present invention. These factors may determine thequality and range of the output of the dispersion measurements. Thefirst factor of interest is the wavelength resolution of themeasurement, the second is the minimum required bandwidth of the source,the third is the measurable bandwidth of the dispersion curve, and thefourth is the test fiber length. The sections that follow discuss howeach of these factors affect the output of the dispersion measurement.

1.3.1 Wavelength Resolution of the Dispersion Measurement

The wavelength resolution of the points in the plot of the dispersionparameter is determined by the minimum step size of the translationstage. With smaller step increments in the translation stage there aresmaller step increments in the plot of the dispersion parameter vs.wavelength. This is because variation of the air path (27) changes thewavelength where the air path (27) and test fiber (17) are balanced andproduces a new interferogram from which the dispersion parameter can bedetermined. Examination of Eq. 13 shows that the first term can beremoved if the group delay in the air path (27) is equal to that in thetest fiber path for the central wavelength, λ_(o) (central wavelength atwhich the group delay in test fiber (17) and air paths (27) arebalanced). The relationship between the air path length (L_(air)) andthe fiber length (L_(f)) at the wavelength λ_(o) is given by Eq. 19:

$\begin{matrix}{L_{air} = {\left( \left. {{n_{eff}\left( \lambda_{o} \right)} - {\lambda_{o}\frac{n_{eff}}{\lambda}}} \right|_{\lambda_{o}} \right)L_{f}}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$

Taking the derivative of L_(air) with respect to λ_(o) and using thedefinition given by Eq. 15:

$\begin{matrix}{\left. \frac{L_{air}}{\lambda} \right|_{\lambda_{o}} = {{\left( \left. {{- \lambda_{o}}\frac{^{2}n_{eff}}{\lambda^{2}}} \right|_{\lambda_{o}} \right)L_{f}} = {{{cD}\left( \lambda_{o} \right)}L_{f}}}} & {{Eq}.\mspace{14mu} 20}\end{matrix}$

Therefore the change of λ_(o) with respect to the change of L_(air) canbe written as

$\begin{matrix}{\frac{\lambda_{o}}{L_{air}} = \frac{1}{{cL}_{f}D}} & {{Eq}.\mspace{14mu} 21}\end{matrix}$

Thus, the relationship between a change in the central (balanced)wavelength and the change in the air path length (L_(air)) is given by:

$\begin{matrix}{{d\; \lambda_{o}} = {d\; L_{air}\frac{1}{{cL}_{f}D}}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

The minimum amount by which the air path (27) can change sets theminimum increment of the central wavelength in the interferogram. Thisamount must be several times smaller than the bandwidth of the source.Thus the minimum step size of the air path (27) sets the wavelengthresolution of the measured dispersion curve. Note the wavelengthresolution is also inversely proportional to the dispersion-lengthproduct of the test fiber (17).

The dependence of the wavelength resolution on the dispersion lengthproduct will now be shown. As a numerical example, for a step size of0.1 μm, assuming a 50-cm-long SMF28™ test fiber, the wavelengthresolution is 0.1 nm, which is sufficient for most applications. As agraphical example the wavelength resolution is plotted against thedispersion-length product of standard SMF28™ fiber.

1.3.2 Minimum Required Source Bandwidth

A minimum number of envelope fringes are required for accuratemeasurements of dispersion. As long as the balanced wavelength, λ₀, andfour other wavelengths corresponding to the peaks (or troughs) of theenvelope fringes are captured within the source bandwidth, B_(source),(FIG. 5), it is sufficient to determine dispersion D(λ₀). It is found inpractice that more accurate measurements require selecting two peaks (ortroughs) on either side of λ₀, as indicated by B_(min) on FIG. 5.

For a given test fiber, the dispersion-length product is fixed.Therefore, the only factor that limits the number of envelope fringes isthe source bandwidth, B_(source). The longer the test fiber (17), or thelarger the dispersion, the more closely spaced the envelope fringes, andhence the smaller the required bandwidth. In order to determine B_(min)quantitatively, it is required to determine the maximum value for thewavelength spacing (λ₂−λ₀), as shown in FIG. 5. From Eq. 13, ignoringthe 3^(rd)-order term, envelope phase difference|φ_(envelope)(λ₁)−φ_(envelope)(λ₀|, which has an upper bound of π, sincethe first trough occurs at λ₁ can be obtained:

$\begin{matrix}{{{{\varphi_{envelope}\left( \lambda_{1} \right)} - {\varphi_{envelope}\left( \lambda_{0} \right)}}} = \left. {2\pi \frac{\left( {\lambda_{1} - \lambda_{0}} \right)^{2}}{{2!}\lambda_{1}}\frac{^{2}n_{eff}}{\lambda^{2}}} \middle| {}_{\lambda_{0}}{L_{f} \leq \pi} \right.} & {{Eq}.\mspace{14mu} 23}\end{matrix}$

Applying the definition of dispersion in Eq. 15, the upper bound of thewavelength spacing (λ₁−λ₀) is:

$\begin{matrix}{{\lambda_{1} - \lambda_{0}} \leq \frac{\lambda_{0}}{\sqrt{{cDL}_{f}}}} & {{Eq}.\mspace{14mu} 24}\end{matrix}$

Next, the wavelength spacing between λ₁ and λ₂ is examined. From 4-5,ignoring the 3^(rd)-order term and applying Eq. 15 gives:

$\begin{matrix}{{\left( {\lambda_{2} - \lambda_{0}} \right)^{2} - \left( {\lambda_{1} - \lambda_{0}} \right)^{2}} \approx \frac{\lambda_{o}^{2}}{{cDL}_{f}}} & {{Eq}.\mspace{14mu} 25}\end{matrix}$

Combining Eqs. 24 and 25, the upper bound for the wavelength spacingλ₂−λ₀ is:

$\begin{matrix}{\left( {\lambda_{2} - \lambda_{0}} \right)^{2} = {\left\lbrack {\left( {\lambda_{2} - \lambda_{1}} \right) + \left( {\lambda_{1} - \lambda_{0}} \right)} \right\rbrack^{2} \leq \frac{2\lambda_{o}^{2}}{{cDL}_{f}}}} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

The minimum required source bandwidth B_(min) should be not less thanthe upper bound of 2(λ₂−λ₀), therefore,

$\begin{matrix}{B_{\min} = {2\sqrt{2}\frac{\lambda_{0}}{\sqrt{{cDL}_{f}}}}} & {{Eq}.\mspace{14mu} 27}\end{matrix}$

It is clear that the dispersion-length product of the test fiber (17)also affects the minimum required bandwidth. Using a similar numericalexample, assuming a 50-cm-long SMF test fiber and 1550 nm as thebalanced wavelength, the minimum required bandwidth is 85 nm.

1. 3. 3 Measurable Bandwidth of the Dispersion Curve B_(mea)

Since each spectral interferogram produces one dispersion value at thebalanced wavelength, λ₀, to obtain dispersion versus wavelength, anumber of interferograms are recorded at various balanced wavelengths bysetting the appropriate air path lengths (27). Since each interferogramshould be taken over a bandwidth of at least B_(min), from FIG. 5 onecan see that the measurable bandwidth of the dispersion curve is thedifference between the available source bandwidth B_(source) and theminimum required bandwidth B_(min), that is,

$\begin{matrix}{B_{mea} = {{B_{source} - B_{\min}} \geq {B_{source} - {2\sqrt{2}\frac{\lambda_{0}}{\sqrt{{cDL}_{f}}}}}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$

Alternatively, if two of the troughs are not required to be on each sideof 4, then the measurable bandwidth B_(mea) can be larger. In order toaccurately determine λ₀, the central fringe (from λ⁻¹ to λ₁ in FIG. 5)is required to be entirely visible within the measured spectral range.Therefore,

$\begin{matrix}{B_{mea} = {{B_{source} - {2\left( {\lambda_{1} - \lambda_{0}} \right)}} \geq {B_{source} - {2\frac{\lambda_{0}}{\sqrt{{cDL}_{f}}}}}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$

Either equation Eq. 28 or 29 give the lower bound for the measurablebandwidth, which assumes the widest possible central fringe. Inpractice, since φ_(envelope)(λ₀) cannot be controlled, the width of thecentral fringe can be anywhere between zero and twice the limit of Eq.29. Therefore, B_(mea) can be as large as B_(source) in certain cases.

Examination of Eq. 28 or 29 shows that increasing the dispersion-lengthproduct of the test fiber (17) increases B_(mea). Note that for a givenmeasurement system, B_(source) is fixed, so the only parameter that canbe used to extend B_(mea) is L_(f). The dispersion length product is, infact, the main independent variable in determining the systemparameters.

The dispersion length-product has been shown to be the main independentvariable in determining the measurable bandwidth and the minimumbandwidth. But the range of this parameter is itself affected by thesource used. The bandwidth of the source determines the minimum fiberlength that can be characterized using this technique and the minimumwavelength step of the source leads to a maximum characterizable fiberlength. The next section discusses how the source bandwidth and minimumwavelength step size affect the range of fiber lengths that can bemeasured using the SAI technique.

1. 3. 4 Minimum Fiber Length

The bandwidth of the source determines the minimum fiber length that canbe characterized using SAI. A smaller fiber length produces a widerspectral interferogram as determined by Eq. 27. Thus in order for acertain fiber length to be characterizable using SAI the interferogramproduced must fit inside the source bandwidth. Therefore the requirementis that,

B_(min)≦B_(source)  Eq. 30

Using Eq. 27:

$\begin{matrix}{L_{f} \geq \frac{8\lambda_{o}^{2}}{{cDB}_{source}^{2}}} & {{Eq}.\mspace{14mu} 31}\end{matrix}$

Note that for a longer fiber there will be a greater measurementbandwidth (according to Eq. 28 or 29) and a higher wavelength resolution(Eq. 22). As a numerical example, for a source bandwidth of 130 nm, theminimum length for a SMF28 fiber is 0.23 m. The minimum fiber length isplotted as a function of the source bandwidth in FIG. 6.

1. 3. 5 Maximum Fiber Length

The SAI method uses the slow-varying envelope function to obtaindispersion. Though the “carrier” fringes are not of interest, they stillneed to be resolved during measurement otherwise the envelope shapecannot be preserved. The carrier fringe spacing is directly affected bythe length of the fiber under test, L_(f). A longer fiber will lead tonarrower carrier fringes.

The minimum step size of the tunable laser, however, sets a limit on theminimum carrier fringe period that can be detected due to aliasing.Since a longer fiber length has a higher frequency carrier this minimumdetectable fringe period results in a limit on the maximum fiber length.The carrier fringe period is the wavelength difference that causes thefast varying phase to shift by 2π. The Fast phase term in Eq. 11 for abalanced air path, L_(air)=N_(g)(λ_(o))L_(f), can be written as:

φ=(k _(o) n _(eff) L _(f) +k _(o) N _(g)(λ_(o))L _(f))  Eq. 32

Using a first order approximation of n_(eff) and N_(g)

N _(g)(λ_(o))≈n _(eff) ≈n  Eq. 33

Where n is the core index, the phase term is written as

$\begin{matrix}{\varphi = \frac{4\pi \; n\; L_{f}}{\lambda_{o}}} & {{Eq}.\mspace{14mu} 34}\end{matrix}$

The fringe period, Δλ, corresponds to a 2π phase shift

$\begin{matrix}{{\Delta\varphi} = {{\frac{4\pi \; n\; L_{f}}{\lambda_{o}^{2}}{\Delta\lambda}} = {2\pi}}} & {{Eq}.\mspace{14mu} 35}\end{matrix}$

Hence,

$\begin{matrix}{{\Delta\lambda} = \frac{\lambda_{o}^{2}}{2n\; L_{f}}} & {{Eq}.\mspace{14mu} 36}\end{matrix}$

In order to detect one fringe accurately, the Nyquist criterion isapplied where at least 2 sample points have to be included in onefringe. This sets the following limit over the fiber length:

$\begin{matrix}{L_{f} \leq \frac{\lambda_{o}^{2}}{4n\; {\Delta\lambda}}} & {{Eq}.\mspace{14mu} 37}\end{matrix}$

where Δλ is the minimum wavelength step size of the tunable laser.

If the fiber length limit is exceeded aliasing occurs.

The preceding analysis assumes that it is necessary to avoid aliasing toensure that all of the peaks of the interferogram are sampled in orderto accurately plot the envelope of the interferogram. It is thisassumption that leads to the upper limit in the fiber length given inEq. 37. This upper limit however can be exceeded by dividing theinterferogram into small window sections and selecting a single point ineach window to plot the envelope. The theory behind this technique,called wavelength windowing, will be explained in detail in the nextsection.

1. 4 The Effect of Wavelength Windowing

The problem with trying to measure a fiber longer than Eq. 37 allows isthat the period of the carrier gets shorter with increasing fiberlength. According to Nyquist theory the sampling period, determined bythe average step size of the tunable laser, must be at least 2 timessmaller than the period of the carrier in order to avoid aliasing. Thisensures that all the sampled peaks of the carrier match the trueenvelope of the interference pattern.

Aliasing is a phenomenon that prevents every peak of the carrier frombeing sampled but it does not mean that some of the peaks in a givenwavelength window range will not be sampled. The interferogram can bedivided into small window sections, as shown in FIG. 7, each containingmany sampled points. Thus when aliasing does occur there will be acertain probability that at least one of the sampling points will landon a peak of the interferogram within each wavelength window (assuming aslow variation in the envelope within that window). Therefore, theenvelope of the interferogram can be plotted under conditions wherealiasing does occur by taking the maximum in each wavelength window andconnecting them together, as shown in FIG. 7.

Detailed statistical analysis (developed in the next section) shows howthe probability that at least one of the peaks will be sampled within awavelength window is determined. This technique shows that the upperlimit in Eq. 37 can be exceeded by many folds by wavelength windowing.

1. 5 Model Development

This technique uses a tunable laser (31) system to sample the peaks ofan interferogram. A real world tunable laser (31) system, however, doesnot step the wavelength with equal step sizes but has a certain standarddeviation in its step size. In order to produce an accurate modeling ofa real world process this variation in the step size of the tunablelaser (31) must be taken into account by the model. The tunable laser(31) system used in the experiments was the Agilent 8164A™ which has anaverage step size of 1 pm and a standard deviation of 0.17 pm asdetermined from the histogram and the Gaussian probability densityfunction (PDF) in FIG. 8.

In order for the model to accurately determine the probability of asampled point matching at least one peak of the carrier wave within acertain wavelength window, certain parameters must be determined. Themodel that will be developed requires knowledge of the fiber length, thewidth of wavelength window, the average step size of the tunable laser,the standard deviation of this step size and the tolerance in detectingthe peak as a percentage of the carrier period.

In this model the fiber length as L_(f), the wavelength window withinwhich it is desired to detect a peak as W, the average step size of thetunable laser as μ, the standard deviation of the step size of thetunable laser as σ and the tolerance in detecting the peak as apercentage of the carrier period as ε can be designated. If λ_(o) is theseparation between the first carrier peak and the maximum samplingprobability density of the first step, as shown in FIG. 9, then thewavelength location of the next maximum sampling probability occurs atλ_(o)+μ and the following one occurs at λ_(o)+2μ and so on. FIG. 9illustrates the probability density functions along with the carrierfunctions.

FIG. 9 also illustrates the fact that even with aliasing, where all thepeaks of the interferogram are not sampled, there is still a chance thatat least one of the peaks of the interferogram will be sampled for agiven wavelength window since the period of the peaks of the carrier isdifferent than the period of the wavelength steps of the tunable laser.Thus, for any given window size there will be a number of peaks of thecarrier.

Assuming the location of the first carrier peak to be at λ₁, as shown inFIG. 9, then the probability that this first peak is sampled by thefirst step of the tunable laser is given by:

$\begin{matrix}{P_{11} = {\int_{\lambda_{1} - \frac{ɛ}{2}}^{\lambda_{1} + \frac{ɛ}{2}}{\frac{1}{\sqrt{2\pi}\sigma}^{({- \frac{{({\lambda - \lambda_{o}})}^{2}}{2\sigma^{2}}})}\ {\lambda}}}} & {{Eq}.\mspace{14mu} 38}\end{matrix}$

Therefore the probability that the first peak is sampled by the firststep is:

$\begin{matrix}{\overset{\_}{P_{11}} = {{1 - P_{11}} = {1 - {\int_{\lambda_{1} - \frac{ɛ}{2}}^{\lambda_{1} + \frac{ɛ}{2}}{\frac{1}{\sqrt{2\pi}\sigma}^{({- \frac{{({\lambda - \lambda_{o}})}^{2}}{2\sigma^{2}}})}{\lambda}}}}}} & {{Eq}.\mspace{14mu} 39}\end{matrix}$

Here ε, shown in FIG. 9, is a fraction of the width of the carrierperiod and this measure translates into a tolerance in the measurementof the peak amplitude.

If N is the number of steps of the tunable laser in a given window sizethen the probability of not sampling the first peak with any of the Nsteps is given by:

$\begin{matrix}\begin{matrix}{\overset{\_}{P_{N}} = {\overset{\_}{P_{11}P_{12}}\mspace{20mu} \ldots \mspace{20mu} \overset{\_}{P_{1\; N}}}} \\{= {\prod\limits_{n = 1}^{N}\; \left\lbrack {1 - {\frac{1}{\sqrt{2\pi}\sigma}{\int_{\lambda_{1} - \frac{ɛ}{2}}^{\lambda_{1} + \frac{ɛ}{2}}{\frac{1}{\sqrt{2\pi}\sigma}^{({- \frac{({\lambda - {({\lambda_{o} + {n\; \mu}})}^{2}}}{2\sigma^{2}}})}{\lambda}}}}} \right\rbrack}}\end{matrix} & {{Eq}.\mspace{14mu} 40}\end{matrix}$

If M is the number of peaks of the carrier in a given window size thenthe probability of not sampling any of the M peaks with any of the Nsteps is given by:

$\begin{matrix}\begin{matrix}{\overset{\_}{P_{NM}} = {\prod\; \overset{\_}{P_{n\; m}}}} \\{= {\prod\limits_{m = 1}^{M}\; \prod\limits_{n = 1}^{N}}} \\{\left\lbrack {1 - {\frac{1}{\sqrt{2\pi}\sigma}{\int_{\lambda_{m} - \frac{ɛ}{2}}^{\lambda_{m} + \frac{ɛ}{2}}{\frac{1}{\sqrt{2\pi}\sigma}^{({- \frac{\lambda - {(\begin{matrix}{\lambda_{o} +} \\{n\; \mu}\end{matrix})}^{2}}{2\sigma^{2}}})}{\lambda}}}}} \right\rbrack} \\{= {\prod\limits_{m = 1}^{M}\; {\prod\limits_{n = 1}^{N}\left\lbrack {1 - {\frac{1}{2}\left\lbrack {{{erf}\left( \Lambda_{+} \right)} - {{erf}\left( \Lambda_{-} \right)}} \right\rbrack}} \right\rbrack}}}\end{matrix} & {{Eq}.\mspace{14mu} 41}\end{matrix}$

Where λ_(m) is the location of the m^(th) peak in the wavelength windowand is given by m k_(i) and Λ₊ and Λ⁻ are the normalized wavelengthparameters given by:

$\begin{matrix}{\Lambda_{m \pm} \equiv \frac{\left( {\lambda_{m} \pm \frac{ɛ}{2}} \right) - \left( {\lambda_{o} + {n\; \mu}} \right)}{\sqrt{2}\sigma}} & {{Eq}.\mspace{14mu} 42}\end{matrix}$

Since the model assumes a fixed relationship between the first carrierpeak and the maximum of the probability density function thisprobability should be averaged for λ_(o) varying over one carrier waveperiod. This gives the probability that no carrier peak is sampled in agiven window for a random alignment between the carrier peaks and themaximum of the probability density function. The result is given as:

$\begin{matrix}{{\langle\overset{\_}{P_{NM}}\rangle} = {\langle{\prod\limits_{m = 1}^{M}\; {\prod\limits_{n = 1}^{N}\left\lbrack {1 - {\frac{1}{2}\left\lbrack {{{erf}\left( \Lambda_{+} \right)} - {{erf}\left( \Lambda_{-} \right)}} \right\rbrack}} \right\rbrack}}\rangle}} & {{Eq}.\mspace{14mu} 43}\end{matrix}$

Thus the probability that at least one of the peaks is sampled for agiven window size is determined as:

$\begin{matrix}{{\langle P\rangle} = {1 - {\langle{\prod\limits_{m = 1}^{M}\; {\prod\limits_{n = 1}^{N}\left\lbrack {1 - {\frac{1}{2}\left\lbrack {{{erf}\left( \Lambda_{+} \right)} - {{erf}\left( \Lambda_{-} \right)}} \right\rbrack}} \right\rbrack}}\rangle}}} & {{Eq}.\mspace{14mu} 44}\end{matrix}$

1.6 Simulation Results

1.6.1 Probability vs. Fiber Length

The probability that at least one peak is sampled in a given windowsize, W, is shown in FIG. 10 as a function of the fiber length, L_(f).The parameters held constant for this simulation are the average stepsize of the tunable laser (31) (μ=1 pm), the window size (W=0.25 nm) andthe tolerance (ε=0.02× average carrier period). The probability isplotted for 3 different cases of the standard deviation in FIG. 10:σ=0.05 pm, which is as close as possible to the σ=0 case (i.e. constantstep size case) using the model since σ=0 leads to a Λ_(m+)=1/0(undefined) in Eq. 42, σ=0.17 pm and σ=1 pm.

FIG. 10 shows some peculiar dips where the probability drops to zero forthe cases where the standard deviation is small (σ=0.05 pm and σ=0.17pm). When the standard deviation is high (σ=1 pm) these dips disappear.FIG. 10 also shows that for higher standard deviation the probabilitycurves drop more quickly to the asymptotic value. Thus a lower standarddeviation in the step size of the tunable laser (31) produces curveswith higher initial probabilities, but large dips in the probabilitycurve where the probability drops to zero. A higher standard deviationin the step size produces curves with lower initial probabilities buteliminates the dips where the probability drops to zero. It is thereforebeneficial to have some amount of variation in the step size of thetunable laser (31) in order to eliminate these dips in the probability.

2: Experimental Results 2.1 Experimental Process

The first step in the experiment is to set up the Single ArmInterferometer and to assemble the control and data acquisition hardware(29). The second step in the experiment is to test the technique byusing it to measure the dispersion of test fibers (17) for which thedispersion curves are known or that can easily be measured usingconventional techniques. To do this, the dispersion curves of SingleMode Fiber (SMF28™) and Dispersion Compensating Fiber (DCF) weremeasured. After careful analysis of the results for the experiments onSMF28™ and DCF the new technique was then used to measure the dispersionof a test fiber (17) that has never before been characterized (twin-holefiber). The entire experimental process for this project is outlined inFIG. 11.

2. 2 Experimental Instrumentation & Specific Limits

The experimental set up is shown in FIG. 11. The tunable laser source(41) and detector (23) used are plug-in modules of the Agilent 8164ALightwave Measurement System™. The tunable laser source (41) has abandwidth of 130 nm centered around 1550 nm, and a minimum averagewavelength step of 1 pm (standard deviation σ=0.17 pm). The unit recordsthe detector (23) readings and the wavelength readings as the tunablelaser source (41) wavelength is swept. The spectral interference patternis then analyzed. An angle-polished connector (25) is used at the launchfiber (15) as shown in FIG. 11 in order to eliminate the reflection fromthis facet. The reflections from the collimating lens (19) surfaces aresuppressed by using an antireflection coated lens. The dispersion of thelens (19) is negligible. The mirror (21) tilt is adjusted to obtainmaximum fringe visibility. The mirror (21) translation is controlledmanually, and the minimum step is approximately 5 μm.

Optionally, the launch fiber (15) may be configured as a polarizationcontroller. This may be accomplished by a number of means known to thoseskilled in the art, such as looping the launch fiber (15) into threecoils. Alternately, the polarization controller may be implemented byplacing a linear polarizer in the air path (27). By providing apolarization controller, the SAI may be operable to measure polarizationmode dispersion.

2. 3 Experiments 2.3.1 Single Mode Fiber

The dispersion properties of SMF28™ are well known and hence it was usedto verify the theory of single arm interferometry. In this experiment a39.5±0. 1 cm piece of the SMF28™ fiber was used in a SAI in order tocharacterize its dispersion. FIG. 12 shows a plot of both theexperimental dispersion parameter points and the simulated dispersion ofSMF28™. From this figure it can be seen that the slope of the measureddispersion points closely match the simulated dispersion curve. Thesimulated dispersion curve for SMF28™ was calculated using thedispersion equation:

$\begin{matrix}{{D(\lambda)} = {\frac{S_{o}}{4}\left\lbrack {\lambda - \frac{\lambda_{o}^{4}}{\lambda^{3}}} \right\rbrack}} & {{Eq}.\mspace{14mu} 45}\end{matrix}$

Where λ₀=1313 nm and S_(o)=0.086 ps/nm-km and D(λ) is measured inps/nm-km.

The wavelength resolution of the measured dispersion curve, asdetermined by Eq. 22, is 2.4 nm. The measurable bandwidth according toEq. 29 is 30 nm, which is the bandwidth actually used, as shown in FIG.12. The standard deviation of the measured dispersion is calculated bytaking the difference between the measured points and a linear fit andthen calculating the standard deviation from the difference. Thestandard deviation is 0.28 ps/nm-km (this corresponds to a relativeerror of 1. 6%). When this standard deviation is multiplied by thelength of the fiber, this translates into a standard deviation of 0.0001ps/nm.

The simulated interference pattern is generated using Eq. 17 and theenvelope of the interference pattern is generated using Eq. 18. In thesimulation a test fiber (17) length of 0.395 m is assumed in order tomatch the experimental conditions. The path length of the air path (27)is determined via a calculation of the effective group index of thefiber was determined to be 1.472469 at the central wavelength, λ_(o),via Eq. 46:

$\begin{matrix}{\frac{\left( {{\kappa (\lambda)}\alpha} \right){J_{l + 1}\left( {{\kappa (\lambda)}a} \right)}}{J_{l}\left( {{\kappa (\lambda)}a} \right)} = \frac{\left( {{\gamma (\lambda)}a} \right){K_{l + 1}\left( {{\kappa (\lambda)}a} \right)}}{K_{l}\left( {{\kappa (\lambda)}a} \right)}} & {{Eq}.\mspace{14mu} 46}\end{matrix}$

Where

κ(λ)=√{square root over (n_(core)(λ)² −n _(eff)(λ)²)}{square root over(n_(core)(λ)² −n _(eff)(λ)²)}

γ(λ)=√{square root over (n_(eff)(λ)² −n _(cladding)(λ)²)}{square rootover (n_(eff)(λ)² −n _(cladding)(λ)²)}  Eq. 47

Note that a is the core size of the fiber and J and K are Besselfunctions of the first and second kind. The locations of equality in Eq.46 determine the values of κ(λ) and γ(λ) as well as a mode of the fiber.The first of these modes is called the fundamental mode of the fiber.The values of n_(core)(λ) and n_(cladding)(λ) are the index of bulkglass with the composition of the core and cladding respectively. Theeffective group index as a function of wavelength in SMF28™ fiber isdetermined using simulation.

2.3.2 Dispersion Compensating Fiber

As a second method of verification, dispersion was measured on a shortpiece of DCF, whose dispersion value is approximately one order ofmagnitude higher than that of SMF28™, and has an opposite sign. A 15.5+0. 1 cm piece of DCF fiber was used, and the measurement results aregiven in FIG. 13. To verify the accuracy of the measurement, dispersionwas also measured on an identical 100±0 5 m DCF using a commercialdispersion measurement system (Agilent 83427A™), which employs the MPStechnique. Again, measured dispersion values are in good agreement withthose measured by the commercial device, though the test fiber (17)length used is almost 3-orders of magnitude smaller.

The standard deviation of the measured dispersion is calculated bytaking the difference between the measured points and a linear fit andthen determining the standard deviation of the difference. The standarddeviation of the measured data is 0.99 ps/nm-km, which corresponds to arelative error of 0.9%. When multiplied by the length of the test fiber(17), this translates into a standard deviation of 0.00015 ps/nm.

Since DCF has negative dispersion values a procedure for determining thesign of the dispersion was developed. By examination of Eq. 22 repeatedbelow for convenience

$\begin{matrix}{{d\; \lambda_{o}} = {d\; L_{air}\frac{1}{{cL}_{f}D}}} & {{Eq}.\mspace{14mu} 48}\end{matrix}$

If the sign of the dispersion is negative then the location of thecentral wavelength will decrease as the path length of the air path (27)is increased. This is a quick method for determining the sign of thedispersion.

2.3.3 Twin-Hole Fiber

Twin-Hole Fiber (THF) has been used in fiber poling to facilitateparametric generation in fibers or making fiber-based electro-opticswitching devices. In such nonlinear applications, dispersion of thefiber is an important parameter to be determined. The dispersionproperties of THF, however, have never been reported. This is partly dueto the lack of uniformity in the diameter of the THF along its length.The fiber has a 3-μm-diameter core and a numerical aperture that ishigher than that of SMF28™. The cross section of a typical THF is shownin FIG. 14.

The core is Ge-doped silica, and has an index similar to that of SMF28™.Therefore, the dispersion of THF is expected to be slightly lower thanthat of SMF28™. Without knowing the magnitude of the dispersion for THF,it is best to choose the largest length of THF available to increase thechance that the minimum bandwidth required for a measurement would fitin the available bandwidth of the tunable laser source. The largestlength of THF available was 45±0. 1 cm. This length of fiber is slightlylonger than the length allowed by Eq. 37 but since the technique ofwavelength windowing described in sections 4.5.1-4.5.3 was used themeasurement of the envelope was still possible in this experiment.

The measurement results from the experiment on THF are given in FIG. 15.The standard deviation of the measured dispersion is calculated bytaking the difference between the measured points and a linear fit andthen calculating the standard deviation from the difference. Thestandard deviation of the measured data is 0.375 ps/nm-km (whichcorresponds to a relative error of 2.9%). When multiplied by the fiberlength, this standard deviation translates into a precision of 0.00017ps/nm. The slightly larger standard deviation compared to those for theSMF and DCF measurement is due to the higher loss in fiber couplingbetween the SMF and the THF, and hence the lower and more noisy signallevel during the THF measurement.

An important aspect of the previous three sections is the errorassociated with the measurement of each point in the dispersionparameter plots. The next section outlines the source and magnitude ofthe error associated with the measurement of the dispersion parameter.

In conclusion, the experimental results of Single Arm Interferometryconfirm the accuracy of the present invention. They show that thedispersion parameter can be calculated from the envelope of the fringepattern produced by the interference of 3 waves in a balanced SAI. Theexperiments on Single mode fiber (SMF28™) and Dispersion CompensatingFiber (DCF) were used to confirm the theory behind the technique andonce the technique was confirmed it was used to measure the unknowndispersion parameter plot for THF. The length of twin-hole fiber used inthe experiment was larger than allowed by Eq. 37 so the technique ofwavelength windowing, described in sections 4.5.1-4.5.3, had to be used.This technique was shown theoretically and via simulation to extend themaximum length of fiber that can be characterized by this technique.Ultimately the largest length of fiber that can be characterized islimited by the largest air path (27) that can be produced in theexperiment and the laser linewidth.

As mentioned, the resolution of balanced spectral interferometry, inparticular, can be improved by replacing the combination broadbandsource and Optical Spectrum Analyzer with a tunable laser (31) anddetector (23) system. Current tunable laser technology allows for abandwidth of 130 nm and a 1 picometer resolution. This improves therange of fiber lengths that can be measured using this technique. Alsoof note is that the use of tunable lasers for dispersion measurement isbecoming more widespread as they decrease in cost.

3: Benefits 3. 1 Significance to Research

The single arm interferometer is an alternative to the Michelson or theMach-Zehnder configuration for interferometric measurements of thedispersion parameter. It is most useful for measurements of thedispersion parameter in short lengths of fiber. The technology may beused to eliminate the need for the arm balancing required by dual arminterferometers and by doing so allow for greater ease in the use ofinterferometric dispersion measurement techniques.

The new interferometer is significant for researchers since it can bestudied and used alongside the earlier types of interferometers like theMichelson, the Mach-Zehnder and the Fabry Perot. This new interferometerprovides researchers with another tool for studying dispersion in shortlength fibers and waveguides which will be useful in the development ofspecialty fibers. These specialty fibers require simple and accurateshort length characterization since they are generally made in verysmall quantities and their geometry tends to vary as a function ofposition along the fiber.

3. 2 Significance to Industry

The new interferometer is significant to industry since it minimizes theneed to compensate for unwanted reflections by eliminating the need fora coupler altogether. As a result this interferometer is a simpler (lessexpensive) interferometric dispersion measurement device capable ofcharacterizing the dispersion of short length optical fiber. As a resultit is a viable commercial competitor to the current Modulation PhaseShift (MPS) based devices currently on the market. The newinterferometer, however, has an advantage over MPS based devices sinceit has the ability to measure short length fiber with high accuracy.

Also, since it can measure short lengths of fiber it has the ability foranother type of measurement as well. Dispersion is a function of bothmaterial and dimensional (waveguide) properties of a fiber but if thedimensions, particularly the diameter of the fiber, vary then thedispersion will vary. If several small sections can be cut from variouspoints on a long length fiber and the dispersion is measured in each ofthem then the variation in the dispersion can be plotted as a functionof position in the fiber. This can then be directly related to thevariation in the fiber diameter. The main point here is that a greatdeal of accuracy in measuring the fiber diameter can be achieved bymeasuring it indirectly via the dispersion and it would be an easy wayfor a fiber drawing company to perform quality control.

Greater commercial interest in this device will enable measurement ofdispersion in smaller lengths of fiber since larger bandwidth tunablelasers will be developed. Also the advancement in the speed of thetunable laser and scanning process will make each measurement faster toobtain.

3.3 Module

One of the most interesting features of a single arm interferometer isthe ease with which it can be built. This ease of construction lendsitself very nicely to economical commercial assembly of a dispersionmeasurement device, such as an add-on module for a tunable laser systemto allow it to make dispersion measurements. A conceptual design of sucha module is illustrated in FIG. 16.

1. An interferometer system for obtaining a measure of the chromaticdispersion of a waveguide comprising: a. a radiation source operable toemit radiation connected to a means for separating incident andreflected waves; b. the means for separating incident and reflectedwaves having an output arm adjacent to a first end of the waveguide; c.the means for separating incident and reflected waves further connectedto a detector; d. a collimating means positioned at a second end of thewaveguide; and e. a reflecting means positioned at a balanced distancefrom the collimating means operable to reflect a test emission from theradiation source back through the collimating means, the waveguide, andthe means for separating incident and reflected waves thereby generatingan interference pattern that is recorded by the detector;
 2. Theinterferometer system as claimed in claim 1 wherein said interferencepattern consists of three waves wherein a first wave is a reflection ofthe test emission from one facet of the waveguide, a second wave is areflection of the test emission from a second facet of the waveguide anda third wave is a reflection of the test emission from the reflectingmeans.
 3. The interferometer system as claimed in claim 1 wherein saidmeans for separating incident and reflected waves is a circulator. 4.The interferometer system as claimed in claim 1 wherein said means forseparating incident and reflected waves is a 2-to-1 coupler.
 5. Theinterferometer system as claimed in claim 1 wherein said interferometeris in the form of a single arm interferometer.
 6. The interferometersystem as claimed in claim 1 wherein said radiation source is a tunablelaser.
 7. The interferometer system as claimed in claim 1 wherein saidoptical detector is an optical spectrum analyser.
 8. The interferometersystem as claimed in claim 1 wherein the output arm of the means forseparating incident and reflected waves comprises a launch waveguideterminating at an angle polished connector.
 9. The interferometer systemas claimed in claim 1 wherein the connecting end of the waveguide is aflat polished connector.
 10. The interferometer system as claimed inclaim 1 wherein the collimating means is a collimating lens.
 11. Theinterferometer system as claimed in claim 1 wherein the reflecting meansis a mirror.
 12. The interferometer system as claimed in claim 8 whereinthe angle polished connector is cleaved at an angle to minimizereflection back to the circulator.
 13. The interferometer system asclaimed in claim 8 wherein the angle polished connector is aligned tothe waveguide using a fastening means.
 14. The interferometer system asclaimed in claim 13 wherein the fastening means is operable to preventdamage to the angled polished connector by minimizing contact with thewaveguide.
 15. The interferometer system as claimed in claim 13 whereinthe fastening means is a fiber connecting pin.
 16. The interferometersystem as claimed in claim 1 wherein the waveguide is selected from agroup consisting of optical fiber, photonic crystal fiber, nanowire,nanofiber and etched waveguide.
 17. The interferometer system as claimedin claim 16 wherein the waveguide is a single mode fiber.
 18. Theinterferometer system as claimed in claim 16 wherein the waveguide is atwin-hole fiber.
 19. The interferometer system as claimed in claim 16wherein the waveguide is a dispersion compensating fiber.
 20. Theinterferometer system as claimed in claim 16 wherein the waveguide is again fiber.
 21. The interferometer system as claimed in claim 1 whereina minimum length of the waveguide for which the measure may be obtainedis limited by a bandwidth of the radiation source.
 22. Theinterferometer system as claimed in claim 21 wherein the bandwidth ofthe radiation source is in the order of hundreds of nanometers and theminimum length of the waveguide is in the order of tens of centimetres.23. The interferometer system as claimed in claim 6 wherein a maximumlength of the waveguide for which the measure may be obtained is limitedby a minimum step size of the tunable laser.
 24. The interferometersystem as claimed in claim 1 wherein the interferometer may bemodularized and inserted into a broadband source.
 25. The interferometersystem as claimed in claim 1 wherein the interferometer may bemodularized and connected to a lightwave measurement system.
 26. Theinterferometer system as claimed in claim 8 operable to obtain a measureof the polarization mode dispersion of a waveguide comprisingmanipulating the launch waveguide such that it forms three coils, eachsaid coil including a 360° turn.
 27. The interferometer system asclaimed in claim 1 operable to obtain a measure of the polarization modedispersion of a waveguide comprising placing a linear polarizer betweenthe collimating means and the reflecting means, said linear polarizeroriented at an angle between 0° and 90° to a path of the test emission.28. An interferometric method for obtaining a measure of the chromaticdispersion of a waveguide comprising the steps of: a. connecting aradiation source to a means for separating incident and reflected waves,said means for separating incident and reflected waves having an outputarm terminating at a connector; b. placing a first facet of thewaveguide adjacent to the connector, c. connecting the means forseparating incident and reflected waves to a detector; d. placing acollimating lens at a second facet of the waveguide; e. positioning areflecting means at a balanced distance from the collimating lens; f.generating a radiation emission from the radiation source; g. recordingan interferogram consisting of three waves with the detector wherein thefirst wave is a reflection of the radiation emission from the firstfacet of the waveguide, the second wave is a reflection of the radiationemission from the second facet of the waveguide, and the third wave is areflection of the radiation emission from the reflecting means; and h.measuring dispersion parameters from the recorded interferogram.
 29. Theinterferometric method as claimed in claim 28 wherein the interferometeris single-arm.
 30. An interferometric method for obtaining a measure ofthe chromatic dispersion of an external waveguide to a modularinterferometer comprising the steps of: a. generating a modularinterferometer including: i. a first input operable to connect anexternal radiation source to an internal means for separating incidentand reflected waves; ii. a second input operable to connect an externaldetector to the internal means for separating incident and reflectedwaves; iii. a duo-input wherein a third input is operable to connect afirst facet of the waveguide to the internal means for separatingincident and reflected waves and wherein a fourth input is operable toplace a second facet of the waveguide in close proximity to an internalcollimating means wherein an internal reflecting means is positioned ata distance to said internal collimating means. b. connecting a firstfacet of the waveguide to the third input; c. connecting a second facetof the waveguide to the fourth input; d. generating a radiation emissionfrom the external radiation source; e. recording an interferogramconsisting of three waves with the external detector wherein a firstwave is a reflection of the radiation emission from the first facet ofthe waveguide, a second wave is a reflection of the radiation emissionfrom the second facet of the waveguide, and a third wave is a reflectionof the radiation emission from the reflecting means; and f. measuringdispersion parameters from the recorded interferogram.
 31. A method forincreasing a maximum length of a waveguide for which chromaticdispersion may be measured using an interferometer comprising: a.generating an interferogram including sampling a radiation intensity ateach of a set of wavelengths, each said wavelength separated by a stepsize of a tunable laser; b. selecting a set of wavelength windows, eachsaid wavelength window including a portion of the interferogramcorresponding to one or more of said wavelengths, the set of wavelengthwindows encompassing the whole of the interferogram, the set ofwavelength windows not overlapping at any given portion of theinterferogram; c. selecting a maximum radiation intensity measured ineach of said wavelength windows; and d. connecting the maximum radiationintensities of each said wavelength window together to form a wavelengthenvelope.
 32. The method as claimed in claim 31 for stabilizing theprobability that the maximum radiation intensity measured in each of thewavelength windows is obtained, for a long length of the waveguide,comprising selecting the tunable laser having a high standard deviationof the step size.